Testing hypotheses on dioptric power.

Transformation of dioptric power from the conventional clinical representation as sphere, cylinder, and axis to the vectorial representation known as the vector h makes it possible to apply formal multivariate statistical methods to dioptric power. Methods are described for testing hypotheses on mean dioptric power and on variance-covariance of dioptric power for one and more than one population. A number of numerical examples are presented. Attention is drawn to the underlying assumption of multivariate normality, to other limitations of the methods, and to pitfalls in the use of the methods. Three-dimensional scatter plots, shown by means of stereo-pair drawings, are useful for detecting departures from normality.